THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

ON TRAVELING-WAVE SOLUTIONS FOR THE SCALING-LAW TELEGRAPH EQUATIONS

ABSTRACT
The aim of the study is to address the scaling-law telegraph equations with the Mandelbrot-scaling-law derivative. The traveling-wave solutions with use of the Kohlrausch-Williams-Watts function are considered in detail. The works are proposed to describe the physical models in complex topology.
KEYWORDS
PAPER SUBMITTED: 2020-05-01
PAPER REVISED: 2020-05-20
PAPER ACCEPTED: 2020-05-27
PUBLISHED ONLINE: 2020-11-27
DOI REFERENCE: https://doi.org/10.2298/TSCI2006861Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Issue 6, PAGES [3861 - 3868]
REFERENCES
  1. Heaviside, O., On the Extra Current, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2 (1876), 9, pp. 135-145
  2. Schwarz, R. J., Friedland, B. Linear Systems, McGraw-Hill, New York. USA, 1965
  3. Cascaval, R. C., et al., Fractional Telegraph Equations, Journal of Mathematical Analysis and Applications, 276 (2002), 1, pp. 145-159
  4. Orsingher, E., Beghin, L., Time-Fractional Telegraph Equations and Telegraph Processes with Brownian Time, Probability Theory and Related Fields, 128 (2004), 1, pp. 141-160
  5. Povstenko, Y., Theories of Thermal Stresses Based on Space-time-fractional Telegraph Equations, Computers & Mathematics with Applications, 64 (2012), 10, pp. 3321-3328
  6. Yang, X.-J. Theory and Applications of Special Functions for Scientists and Engineers, Springer Nature, New York, USA, 2021
  7. Yang, X.-J., et al., General Fractional Derivatives with Applications in Viscoelasticity, Academic Press, New York, USA, 2020
  8. Yang, X.-J., New General Calculi with Respect to Another Functions Applied to Describe the Newton-like Dashpot Models in Anomalous Viscoelasticity, Thermal Science, 23 (2019), 6B, pp. 3751-3757
  9. Yang, X. J., et al., New Mathematical Models in Anomalous Viscoelasticity from the Derivative with Respect to Another Function View Point, Thermal Science, 23 (2019), 3A, pp. 1555-1561
  10. Yang, X. J., New Non-Conventional Methods for Quantitative Concepts of Anomalous Rheology, Thermal Science, 23 (2019), 6B, pp. 4117-4127
  11. Leibniz, G. W., Memoir Using the Chain Rule, Cited in TMME 7:2&3, p. 321-332, 2010, 1676
  12. Riemann, B. Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe, Dieterich, Göttingen, 1867
  13. Stieltjes, T. J., Recherches Sur les Fractions Continues, Comptes Rendus de l’Académie des Sciences Series I - Mathematics, 118 (1894), pp. 1401-1403
  14. Sommerer, J. C., et al., Experimental Confirmation of the Scaling Theory for Noise-Induced Crises, Physical Review Letters, 66 (1991), 15, pp. 1947
  15. Werner, J. P., et al., Crisis and Stochastic Resonance in Shinriki’s Circuit, Physica D: Nonlinear Phenomena, 237 (2008), 6, pp. 859-865
  16. Mandelbrot. B., How Long is the Coast of Britain? Statistical Self-similarity and Fractional Dimension, Science, 156 (1967), 3775, pp. 636-638
  17. Kohlrausch, R., Theorie des Elektrischen Rckstandes in der leidener Flasche, Annalen der Physik, 167 (1854), 2, pp. 179-214
  18. Williams, G., Watts, D. C., Non-Symmetrical Dielectric Relaxation Behaviour Arising from a Simple Empirical Decay Function, Transactions of the Faraday society, 66 (1970), pp. 80-85

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence